A wave gear device is provided with a rigid internally toothed gear, a flexible externally toothed gear, and a wave generator; the wave generator typically having an elliptical outline. The wave generator causes the flexible externally toothed gear to flex into an elliptical shape, and both ends along the major axis of the elliptical shape mesh with the rigid internally toothed gear. The number of teeth of the flexible externally toothed gear is 2n less (n is a positive number) than the number of teeth in the rigid internally toothed gear. When the wave generator is caused to rotate via a motor or the like, the position in which both gears mesh moves in the circumferential direction, and counter-rotation corresponding to the difference in the number of teeth on each gear occurs between the gears. There is known a wave gear device referred to as a flat wave gear device.
In a flat wave gear device, in order to output the counter-rotation of the rigid internally toothed gear and the flexible externally toothed gear, two rigid internally toothed gears are disposed in parallel in a coaxial state, with one of the rigid internally toothed gears having the same number of teeth as the flexible externally toothed gear and the other rigid internally toothed gear having 2n more teeth than the flexible internally toothed gear. One of the rigid internally toothed gears is secured so as not to rotate, and rotation is output from the other rigid internally toothed gear.
From the original invention of the wave gear device by C. W. Musser (Patent Document 1) up to the present, a variety of inventions have been proposed by Musser and numerous other researchers. However, these inventions primarily relate to a tooth profile for cases when the flexible externally toothed gear and the rigid internally toothed gear have a different number of teeth.
Very few proposals have been made in regard to a tooth profile for a flexible externally toothed gear and a rigid internally toothed gear in the flat wave gear device when there is no difference in the number of teeth. No proposals have been made since those made in Patent Documents 2 and 3.    [Patent Document 1] U.S. Pat. No. 2,906,143    [Patent Document 2] JP-B 38-9157    [Patent Document 3] JP-B 2503027
At present, in order for perfect zero backlash to be achieved in a flat wave gear device, it is necessary for there to be zero backlash on both sides; i.e., the side on which the flexible externally toothed gear and the rigid internally toothed gear have different numbers of teeth, and the side where the gears have the same number of teeth. Particularly in the latter case, no adequate investigations have yet to be made into a tooth profile that accounts for the actual number of teeth.